Determine how many solutions exist for the system of equations. ${-2x+y = 8}$ ${2x-y = -8}$
Solution: Convert both equations to slope-intercept form: ${-2x+y = 8}$ $-2x{+2x} + y = 8{+2x}$ $y = 8+2x$ ${y = 2x+8}$ ${2x-y = -8}$ $2x{-2x} - y = -8{-2x}$ $-y = -8-2x$ $y = 8+2x$ ${y = 2x+8}$ Just by looking at both equations in slope-intercept form, what can you determine? ${y = 2x+8}$ ${y = 2x+8}$ Both equations have the same slope and the same y-intercept, which means the lines would completely overlap. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ Since any solution of ${-2x+y = 8}$ is also a solution of ${2x-y = -8}$, there are infinitely many solutions.